A comprehensive study on vibration and buckling of orthotropic double-layered graphene sheets under hygrothermal loading with different boundary conditions

This paper deals with the vibration and buckling behaviour of orthotropic double -layered graphene sheets with various boundary conditions in a hygrothermal environment. Two graphene sheets are coupled by an elastic media and also limited to the external Pasternak elastic foundations. The governing equations of motion and equilibrium are derived using Hamilton's principle and then solved using Galerkin's method. The general equations for transverse vibration and buckling of orthotropic double-layered graphene sheets subjected to in-plane edge hygrothemal loadings are formulated on the basis of Eringen's differential nonlocal elastic law and the new first order shear deformation theory. The accuracy of the present solutions is demonstrated by comparison with solutions available in the literature. Numerical results are presented to show variations of the frequency and critical buckling load corresponding to various values of the nonlocal parameter, temperature rise, moisture rise, elastic foundation parameter, and aspect ratio. Also, seven different boundary conditions are discussed in the paper.